The use of acoustic (e.g., audible and/or ultrasonic) measurement systems in prior art downhole applications, such as logging while drilling (LWD) and wireline logging applications is well known. Such acoustic measurement systems are utilized in a variety of downhole applications including, for example, borehole caliper measurements, measurement of drilling fluid properties, and the determination of various physical properties of a formation. In one application, acoustic waveforms may be generated at one or more transmitters deployed in the borehole. The acoustic responses may then be received at an array of longitudinally spaced receivers deployed in the borehole. Acoustic logging in this manner provides an important set of borehole data and is commonly used in both LWD and wireline applications to determine compressional and shear wave velocities (also referred to as slowness) of a formation.
It will be appreciated that the terms slowness and velocity are often used interchangeably in the art. They will likewise be used interchangeably herein with the understanding that they are inversely related to one another and that the measurement of either may be converted to the other by simple mathematical calculations. Additionally, as used in the art, there is not always a clear distinction between the terms LWD and MWD. Generally speaking MWD typically refers to measurements taken for the purpose of drilling the well (e.g., navigation) whereas LWD typically refers to measurements taken for the purpose of analysis of the formation and surrounding borehole conditions. Nevertheless, these terms are herein used synonymously and interchangeably.
Procedures for determining compressional and shear wave velocities are known in the prior art. In so-called “fast” formations, in which the shear wave velocity in the formation is greater than a speed of sound in the drilling fluid (drilling mud), the compressional and shear wave velocities may be directly determined from the received waveforms by well established techniques, such as semblance or phase velocity algorithms. However, in so-called “slow” formations, in which the shear wave velocity of the formation is less than the compressional wave velocity of the drilling fluid, direct determination of the shear wave velocity is typically not possible since the shear waves in the formation do not generally refract back into the borehole. Nevertheless, the shear wave velocity remains an important parameter and its determination is desirable.
As such, indirect methodologies have been developed to estimate shear wave velocity in acoustically slow formations. For example, the phase velocity of guided borehole modes, such as Stoneley (monopole), flexural (dipole), and screw (quadrupole) waves may be measured and utilized to estimate a formation shear velocity via known dispersion correction algorithms. The borehole wave velocities are known to depend not only on the formation shear velocity but also on mandrel properties (e.g., modulus) and eccentricity, drilling fluid density and velocity, borehole diameter, frequency, and formation density and compressional velocity. While such dispersion corrections have been successfully utilized in certain applications, in practice, one or more of the above mentioned properties are often not known with a high degree of accuracy, which reduces the accuracy of an estimate of the formation shear velocity. Moreover, properly identifying the detected borehole wave mode (e.g., Stoneley, flexural, or screw waves) can be problematic and misidentification of that mode tends to introduce further errors into the estimated formation shear velocity.
Other indirect methodologies for determining the formation shear velocity in acoustically slow formations typically include transmitting and/or sensing relatively pure borehole guided modes (e.g., Stoneley, flexural, and screw waves). For example, in conventional wireline logging applications, broad bandwidth, dipole logging tools were developed to produce an estimate of shear wave velocity in acoustically slow formations. Dipole (flexural) acoustic waves are known to asymptotically approach the formation shear wave velocity at low frequencies (e.g., from about 1 to about 3 kHz). Thus, in conventional wireline acoustic logging applications, the formation shear wave velocity may be determined from the low frequency portion of the dipole waveform. However, such dipole logging techniques are not typically suitable for LWD applications owing to potentially significant tool wave interference. In wireline applications, tool waves may be reduced via various tool configurations, such as slotted sleeves, isolation joints, and flexible tool structures. In LWD, tool waves tend to be carried by the comparatively stiff tool body, which is essentially the drill string, and thus tend not to be easily mitigated. Additionally, the presence of the drill string in the borehole and tool eccentricity in the borehole tends to alter the propagation modes of the acoustic energy, making it particularly difficult to transmit pure dipole waves. Further, drill bit noise tends to significantly reduce the signal to noise ratio in the low frequency range of interest. As such, deriving formation shear wave velocities from LWD data is not nearly as straightforward as in wireline applications.
In LWD applications there seems to be a trend in the art towards using broadband quadrupole (screw) waveforms (see, for example, Tang, et al., in Petrophysics, vol. 44, pgs. 79-90, 2003). Such quadrupole waveforms have been shown, for some tool configurations, to have a cut-off frequency below which tool wave propagation is substantially eliminated. It is thus apparent in the prior art that the use of quadrupole acoustic signals may be advantageous for determining shear wave velocities in LWD applications. However, the use of quadrupole waveforms tends to introduce other potential difficulties. For example, generating and receiving a relatively pure quadrupole acoustic signal typically requires complex segmented transmitters and receivers. Such transmitters and receivers typically further require highly precise phasing (timing) of the various segments to produce relatively pure quadrupole acoustic signals and to suppress other modes (e.g., monopole and dipole). The difficulty in generating such acoustic signals may be further exacerbated by tool eccentricity in the borehole (e.g., in deviated wells where the tool often lies on or near the low side of the borehole).
Therefore, there exists a need for improved methods for determining a shear wave velocity of a subterranean formation that address one or more of the shortcomings described above. Such methods may, for example, be advantageous in analysis of acoustically slow formations. In particular, it will be appreciated that a direct method that does not depend on dispersion corrections (or other estimation techniques) would be advantageous in that it provides for independent determination of the shear wave velocity and may therefore increase accuracy. Furthermore, a method that is not dependent on isolating dipole or quadrupole waveforms (for example), in the transmission or reception thereof, would also be advantageous, since many of the above stated disadvantages would be obviated.